Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session D35: Suspensions II: Fluid-Particle Interactions |
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Room: 406 |
Sunday, November 24, 2013 2:15PM - 2:28PM |
D35.00001: On the motion of a neutrally buoyant cylinder in simple shear flow Tsorng-Whay Pan, Shih-Di Chen, Shih-Lin Huang, Chin-Chou Chu, Chien-Cheng Chang We have investigated the motion of a neutrally buoyant (NB) cylinder of circular or elliptic shape in simple shear flow by direct numerical simulation. The numerical results are validated by the comparisons with existing theoretical, experimental and numerical results. When placing a NB cylinder of either shape away from the centerline initially, it may migrate to an equilibrium position between the centerline and the wall, not the centerline, depending on the particle Reynolds number. Unlike the circular cylinder, the elliptic shape cylinder can migrate toward the without rotating at the higher particle Reynolds number due to the balanced torque from two sides. [Preview Abstract] |
Sunday, November 24, 2013 2:28PM - 2:41PM |
D35.00002: Rotation of porous ellipsoids in simple shear flows Hassan Masoud, Howard A. Stone, Michael J. Shelley We study theoretically the dynamics of porous ellipsoids rotating in simple shear flows. We use the Brinkman-Debye-Bueche (BDB) model to simulate flow within and through particles and solve the coupled Stokes-BDB equations to calculate the overall flow field and the rotation rate of porous ellipsoids. Our results show that the permeability has little effect on the rotational behavior of particles, and that the Jeffery's prediction of the angular velocity of impermeable ellipsoids in simple shear flows remains an excellent approximation, if not an exact one, for porous ellipsoids. We also examine the orientational diffusion of permeable ellipses and spheroids in the absence of a background flow. Employing an appropriate scaling, we present approximate expressions for the orientational diffusion of ellipses and spheroids. Our findings can serve as basis for developing a suspension theory for non-spherical porous particles. [Preview Abstract] |
Sunday, November 24, 2013 2:41PM - 2:54PM |
D35.00003: Dynamics of a Janus droplet in a linear shear flow Misael D\'Iaz-Maldonado, Andrey Ivantsov, Sergey Shklyaev, Ubaldo M. C\'ordova-Figueroa Janus droplet (JD) is an object with promising applications in the design of smart materials, microfluidics, drug delivery, etc. Despite numerous experimental works, theoretical aspects of JD dynamics remain almost unstudied. Our recent paper [Phys. Fluids, 2013 (accept. for publ.)] was devoted to the generalization of the classic Hadamard--Rybczynski problem, a flow past a droplet in a constant flow. However, in most applications, a JD is subject to a nonuniform flow; the simplest case of such a flow is linear. A perfect JD -- a combination of two hemispherical domains -- is considered; the interfaces are assumed nondeformable. In this case semianalytical solution is valid in terms of series with respect to Lamb's functions. First, we study the rotation of JD around the axis belonging to the internal interface and couple the angular velocity of the internal interface with the viscous torque imposed on JD. This problem, in particular, allows calculating a characteristic time of JD turn under an external torque. Then, the dynamics of JD in a 1D shear flow is analyzed. For arbitrary orientation of JD with respect to the external velocity field and its gradient, the problem is decomposed into five primitive problems. The force and torque for each of these cases are found. [Preview Abstract] |
Sunday, November 24, 2013 2:54PM - 3:07PM |
D35.00004: Numerical simulation of Stokes flow around particles via a hybrid Finite Difference-Boundary Integral scheme Amitabh Bhattacharya An efficient algorithm for simulating Stokes flow around particles is presented here, in which a second order Finite Difference method (FDM) is coupled to a Boundary Integral method (BIM). This method utilizes the strong points of FDM (i.e. localized stencil) and BIM (i.e. accurate representation of particle surface). Specifically, in each iteration, the flow field away from the particles is solved on a Cartesian FDM grid, while the traction on the particle surface (given the the velocity of the particle) is solved using BIM. The two schemes are coupled by matching the solution in an intermediate region between the particle and surrounding fluid. We validate this method by solving for flow around an array of cylinders, and find good agreement with Hasimoto's (J. Fluid Mech. 1959) analytical results. [Preview Abstract] |
Sunday, November 24, 2013 3:07PM - 3:20PM |
D35.00005: Shear-Induced Diffusion of Cubic Colloids Steven Hudson, John Royer, Daniel Blair Particles in many industrially relevant fluid suspensions have directional or anisotropic interactions, yet it is not understood how these interactions influence particle self-association or the rheology of a suspension. We therefore use confocal rheometry to study simultaneously the micro-scale particle motion and macro-scale rheology of a model colloidal suspension. Specifically, we study mono-disperse, hollow, silica cubes exhibiting well-characterized, well-controlled and tunable directional interactions. Tracking the 3-D position and orientation of the cubes as they move under steady shear, we characterize the packing structure and shear-induced diffusion of the cubes varying the shear rate, packing density, and depletion-induced attraction. [Preview Abstract] |
Sunday, November 24, 2013 3:20PM - 3:33PM |
D35.00006: Shear-induced diffusion of non-Brownian suspensions using a colored noise Fokker-Planck equation Laura Lukassen, Martin Oberlack In the Literature, shear-induced diffusion resulting from hydrodynamic interactions between particles, is described as a long-time diffusion. In contrast to the well-known Brownian diffusion which is described by a white noise force, several authors report that the former type of diffusion exhibits the particularity of a much longer correlation time of velocities. Further, Fokker-Planck equations describing this process of shear-induced diffusion have mostly been derived in position space. We present a considerably extended framework of the shear-induced diffusion problem, which essentially relies on the Markov process assumption under the consideration of long correlation times. Applying the mathematical machinery of Markov processes and Fokker-Planck equations, we conclude that this process may only be properly modelled by a Fokker-Planck approach if written in both position and velocity space. With this complementation we observe, that the long correlation times enter as a colored noise velocity. As a result, the Fokker-Planck equation also needs to be extended and we derive the Fokker-Planck equation for the shear-induced diffusion problem following the definitions of a colored noise Fokker-Planck equation. [Preview Abstract] |
Sunday, November 24, 2013 3:33PM - 3:46PM |
D35.00007: Particle drifts in semi-dilute suspensions of highly viscous droplets Hugues Bodiguel, Florinda Schembri, Vincent Mansard, Annie Colin Though already the focus of many experimental and theoretical work, the origin and features of particle migration of semi-dilute suspensions is still in debate. Shear induced cross-stream migration is emphasized in microfluidic flows where high gradients of shear rate are obtained. We study suspensions made of highly viscous droplets in an index matched liquid as a model system. Particle deformation could be neglected, similarly to contact forces that are thought to play a role in suspensions of solid particles. In this work, we focus on a feature of particle migration which has been scarcely described, the particle drift in the flow direction. For that purpose, we developed a technique based on fluorescence photobleaching which enables us to measure simultaneously the particle and suspending fluid velocities. Particles are immersed in a solution containing fluorescein. Thanks to confocal microscopy, we follow the displacement of a bleached line together with the displacement of the particles. The results show that the particle velocity is generally lower than that of the suspending fluid, in a wide range of concentrations from 5 to 40\%. Besides, we also observe a cross-stream migration that is quantified thanks to a balance with buoyancy and compared to existing theories. [Preview Abstract] |
Sunday, November 24, 2013 3:46PM - 3:59PM |
D35.00008: Arbitrary Lagrangian-Eulerian simulations of particle and bubble dynamics in non-Newtonian fluids Pengtao Yue Fluid rheology affects particle-bubble interaction in various ways. For example, it modifies the migration of a single particle and a single bubble as well as the film drainage when they get close. In this talk, we will investigate these non-Newtonian effects using an arbitrary Lagrangian-Eulerian method which simultaneously tracks rigid particle surfaces and deformable bubble surfaces. The gas motion inside each bubble is neglected, and we only consider the bubble pressure which is determined by the isothermal ideal gas law. The particle motion and the fluid motion are solved in a unified Galerkin finite-element framework, in which the hydrodynamic forces and moments between the particle and the surrounding fluid cancel out. Mesh refinement is enforced where the surface curvature is high and where two boundary segments are close; the latter guarantees a sufficient resolution of the film drainage process. Numerical results on bubble migration and particle-bubble interaction in viscoelastic fluids and shear-thinning fluids will be presented. [Preview Abstract] |
Sunday, November 24, 2013 3:59PM - 4:12PM |
D35.00009: Rheological properties of suspensions of bubbles in a yield stress fluid Lucie Ducloue, Guillaume Ovarlez, Xavier Chateau, Olivier Pitois, Julie Goyon We study the macroscopic response under shear of suspensions of bubbles in yield stress fluids. Model suspensions are prepared by mixing a monodisperse foam with a concentrated oil in water emulsion, both having the same continuous phase of a surfactant solution. The interstitial concentrated emulsion behaves as a solid viscoelastic material below a critical stress, and as a shear-thinning fluid above this yield stress. We measure the change in the macroscopic response (elastic modulus, yield stress, non-linear viscosity) due to the addition of bubbles to the fluid. We find that for a given emulsion, the elastic modulus is a decreasing function of the gas volume fraction $\phi $, this decrease being all the sharper as the bubbles are big. We also observe that the yield stress of most studied materials is not modified by the presence of bubbles, whereas the non-linear viscosity during flow increases with $\phi $. We show that those apparently contradictory changes in the behaviour are ruled by the deformability of the bubbles in the fluid. To quantify this effect, we introduce capillary numbers which compare the stresses exerted on a bubble during a measurement to the stresses due to surface tension. We thus compute an elastic capillary number in the solid regime, a plastic capillary number at the yield stress and a viscous capillary number during flow. Those numbers are very different in the solid and in the liquid regimes, explaining why the elastic, plastic and viscous properties do not follow the same evolution. Our results are quantitatively well predicted by a micromechanical approach. [Preview Abstract] |
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